Workspace /E4 Mortgage-Backed Securities
E4

Mortgage-Backed Securities Basics

See how prepayment shapes a mortgage pass-through: monthly cash flows split into scheduled principal, prepayment and interest under a PSA or CPR speed or a refinancing model, with weighted-average life, yield and duration at several speeds, and the price as rates move.

Learning focus: contraction and extension risk, and why MBS lag Treasuries when rates fall.

Pool
%
%
mo
mo
Prepayment
%
bp

The refinancing model is a teaching S-curve: CPR rises from 6% toward 41% as the WAC climbs above the mortgage rate, seasoned over 30 months.

Yield
5.906%
bond-equivalent, at 101.000
Weighted-average life
8.55 years
stated maturity 29.8 years
Modified duration
5.88
cash flows held fixed
Effective duration
4.79
refinancing model, ±50 bp
Effective convexity
−266.2
Prepaid over the life
78.6%
78,577,116
Cash flows by year

Investors receive the net coupon on the remaining balance, the scheduled principal of the level mortgage payments, and every prepayment. The monthly table is below.

When rates move

If mortgage rates fall 200bp, refinancing pushes the CPR to about 33% and the average life contracts from 7.1 to 3.4 years: you get principal back at par just when it would be worth more, so the price rises only to 106.55 against 112.47 for fixed cash flows. If they rise 200bp, prepayments slow to about 7% and the life extends to 10.8 years, so you hold more of a below-market coupon for longer. That is negative convexity: it is why MBS lag Treasuries in a rally.

The rates that discount the cash flows and the mortgage rate move together, and prepayments follow the refinancing model. CPRs shown are for a seasoned pool.

Yield and duration at several speeds
PSAWeighted-average lifeYield at 101.000Modified duration
5014.53 yrs5.959%8.61
10011.29 yrs5.937%7.19
1658.55 yrs5.906%5.88
2506.39 yrs5.865%4.75
4004.40 yrs5.794%3.55
6003.15 yrs5.705%2.70

Bought above par, faster prepayment returns par sooner and cuts the yield. A quoted MBS yield is only as good as the speed assumed behind it.

Monthly cash flows
MonthBalanceCPRInterestScheduled principalPrepaymentCash flow
1100,000,0001.32%500,00092,130110,569702,699
299,797,3011.65%498,98792,526138,142729,654
399,566,6331.98%497,83392,898165,640756,372
499,308,0952.31%496,54093,246193,041782,828
599,021,8082.64%495,10993,569220,321808,999
698,707,9182.97%493,54093,866247,457834,862
798,366,5953.30%491,83394,138274,425860,396
897,998,0323.63%489,99094,383301,203885,577
997,602,4463.96%488,01294,603327,768910,383
1097,180,0754.29%485,90094,795354,097934,793
1196,731,1824.62%483,65694,961380,168958,785
1296,256,0534.95%481,28095,100405,959982,339
1395,754,9955.28%478,77595,211431,4461,005,433
1495,228,3375.61%476,14295,295456,6101,028,047
1594,676,4325.94%473,38295,352481,4281,050,162
1694,099,6526.27%470,49895,380505,8801,071,758
1793,498,3926.60%467,49295,381529,9451,092,818
1892,873,0666.93%464,36595,353553,6031,113,322
1992,224,1097.26%461,12195,298576,8351,133,253
2091,551,9777.59%457,76095,214599,6211,152,595
2190,857,1427.92%454,28695,102621,9421,171,330
2290,140,0988.25%450,70094,962643,7821,189,444
2389,401,3548.58%447,00794,794665,1211,206,922
2488,641,4398.91%443,20794,597685,9441,223,749
2587,860,8979.24%439,30494,373706,2351,239,912
2687,060,2899.57%435,30194,121725,9771,255,399
2786,240,1929.90%431,20193,841745,1551,270,197
2885,401,1969.90%427,00693,533737,9011,258,439
2984,569,7639.90%422,84993,226730,7111,246,786
3083,745,8259.90%418,72992,920723,5871,235,237
3182,929,3189.90%414,64792,615716,5271,223,789
3282,120,1759.90%410,60192,312709,5311,212,443
3381,318,3339.90%406,59292,009702,5981,201,198
3480,523,7269.90%402,61991,707695,7271,190,053
3579,736,2929.90%398,68191,406688,9181,179,006
3678,955,9689.90%394,78091,106682,1711,168,057
3778,182,6909.90%390,91390,808675,4851,157,206
3877,416,3989.90%387,08290,510668,8591,146,451
3976,657,0299.90%383,28590,213662,2931,135,791
4075,904,5229.90%379,52389,917655,7871,125,226
4175,158,8189.90%375,79489,622649,3391,114,755
4274,419,8579.90%372,09989,328642,9501,104,377
4373,687,5799.90%368,43889,035636,6181,094,091
4472,961,9269.90%364,81088,743630,3441,083,897
4572,242,8399.90%361,21488,452624,1261,073,793
4671,530,2619.90%357,65188,162617,9651,063,778
4770,824,1349.90%354,12187,873611,8601,053,853
4870,124,4019.90%350,62287,584605,8101,044,016
4969,431,0079.90%347,15587,297599,8141,034,267
5068,743,8969.90%343,71987,011593,8731,024,604
5168,063,0119.90%340,31586,725587,9861,015,027
5267,388,2999.90%336,94186,441582,1531,005,535
5366,719,7069.90%333,59986,157576,372996,128
5466,057,1779.90%330,28685,875570,643986,804
5565,400,6589.90%327,00385,593564,967977,564
5664,750,0989.90%323,75085,312559,342968,405
5764,105,4439.90%320,52785,033553,769959,328
5863,466,6429.90%317,33384,754548,245950,332
5962,833,6439.90%314,16884,476542,772941,416
6062,206,3959.90%311,03284,199537,349932,580
6161,584,8479.90%307,92483,922531,975923,822
6260,968,9509.90%304,84583,647526,650915,142
6360,358,6529.90%301,79383,373521,374906,540
6459,753,9069.90%298,77083,099516,145898,014
6559,154,6629.90%295,77382,827510,964889,564
6658,560,8719.90%292,80482,555505,830881,190
6757,972,4869.90%289,86282,284500,743872,890
6857,389,4599.90%286,94782,014495,702864,664
6956,811,7429.90%284,05981,745490,707856,511
7056,239,2899.90%281,19681,477485,758848,432
7155,672,0549.90%278,36081,210480,854840,424
7255,109,9909.90%275,55080,944475,994832,488
7354,553,0529.90%272,76580,678471,179824,623
7454,001,1959.90%270,00680,413466,408816,827
7553,454,3739.90%267,27280,150461,680809,102
7652,912,5439.90%264,56379,887456,996801,445
7752,375,6619.90%261,87879,625452,354793,857
7851,843,6829.90%259,21879,364447,755786,337
7951,316,5639.90%256,58379,103443,198778,884
8050,794,2629.90%253,97178,844438,682771,497
8150,276,7379.90%251,38478,585434,208764,177
8249,763,9449.90%248,82078,327429,774756,922
8349,255,8429.90%246,27978,071425,382749,731
8448,752,3909.90%243,76277,814421,029742,605
8548,253,5469.90%241,26877,559416,716735,543
8647,759,2719.90%238,79677,305412,443728,544
8747,269,5239.90%236,34877,051408,209721,608
8846,784,2639.90%233,92176,799404,014714,734
8946,303,4519.90%231,51776,547399,857707,921
9045,827,0479.90%229,13576,296395,738701,169
9145,355,0139.90%226,77576,045391,657694,478
9244,887,3119.90%224,43775,796387,614687,846
9344,423,9019.90%222,12075,547383,608681,274
9443,964,7469.90%219,82475,299379,638674,761
9543,509,8089.90%217,54975,052375,705668,307
9643,059,0519.90%215,29574,806371,808661,910
9742,612,4369.90%213,06274,561367,947655,570
9842,169,9289.90%210,85074,316364,122649,288
9941,731,4909.90%208,65774,073360,331643,061
10041,297,0869.90%206,48573,830356,576636,891
10140,866,6809.90%204,33373,587352,855630,776
10240,440,2379.90%202,20173,346349,169624,716
10340,017,7239.90%200,08973,106345,516618,710
10439,599,1019.90%197,99672,866341,897612,758
10539,184,3399.90%195,92272,627338,311606,860
10638,773,4019.90%193,86772,388334,759601,014
10738,366,2539.90%191,83172,151331,239595,221
10837,962,8639.90%189,81471,914327,752589,481
10937,563,1979.90%187,81671,679324,297583,791
11037,167,2219.90%185,83671,443320,874578,153
11136,774,9049.90%183,87571,209317,482572,566
11236,386,2139.90%181,93170,975314,122567,029
11336,001,1159.90%180,00670,743310,793561,541
11435,619,5799.90%178,09870,511307,495556,104
11535,241,5739.90%176,20870,279304,227550,715
11634,867,0679.90%174,33570,049300,990545,374
11734,496,0289.90%172,48069,819297,782540,082
11834,128,4279.90%170,64269,590294,605534,837
11933,764,2329.90%168,82169,362291,456529,639
12033,403,4149.90%167,01769,134288,337524,489
12133,045,9429.90%165,23068,908285,247519,384
12232,691,7879.90%163,45968,682282,186514,326
12332,340,9209.90%161,70568,456279,153509,314
12431,993,3119.90%159,96768,232276,148504,346
12531,648,9319.90%158,24568,008273,171499,424
12631,307,7529.90%156,53967,785270,222494,545
12730,969,7469.90%154,84967,562267,300489,711
12830,634,8839.90%153,17467,341264,405484,921
12930,303,1379.90%151,51667,120261,538480,173
13029,974,4799.90%149,87266,900258,697475,469
13129,648,8839.90%148,24466,680255,882470,807
13229,326,3209.90%146,63266,462253,094466,187
13329,006,7649.90%145,03466,244250,332461,609
13428,690,1899.90%143,45166,026247,595457,073
13528,376,5679.90%141,88365,810244,884452,577
13628,065,8729.90%140,32965,594242,199448,122
13727,758,0809.90%138,79065,379239,538443,708
13827,453,1629.90%137,26665,164236,903439,333
13927,151,0959.90%135,75564,951234,292434,998
14026,851,8539.90%134,25964,738231,705430,702
14126,555,4109.90%132,77764,525229,143426,445
14226,261,7429.90%131,30964,314226,604422,227
14325,970,8249.90%129,85464,103224,090418,047
14425,682,6319.90%128,41363,892221,599413,904
14525,397,1409.90%126,98663,683219,131409,800
14625,114,3269.90%125,57263,474216,687405,732
14724,834,1669.90%124,17163,266214,265401,702
14824,556,6359.90%122,78363,058211,866397,708
14924,281,7109.90%121,40962,851209,490393,750
15024,009,3699.90%120,04762,645207,136389,828
15123,739,5879.90%118,69862,440204,804385,942
15223,472,3439.90%117,36262,235202,494382,091
15323,207,6149.90%116,03862,031200,206378,275
15422,945,3779.90%114,72761,827197,940374,494
15522,685,6099.90%113,42861,625195,695370,747
15622,428,2909.90%112,14161,422193,471367,034
15722,173,3979.90%110,86761,221191,268363,355
15821,920,9099.90%109,60561,020189,085359,710
15921,670,8039.90%108,35460,820186,924356,098
16021,423,0609.90%107,11560,620184,782352,518
16121,177,6579.90%105,88860,422182,661348,971
16220,934,5749.90%104,67360,223180,561345,457
16320,693,7909.90%103,46960,026178,479341,974
16420,455,2849.90%102,27659,829176,418338,524
16520,219,0379.90%101,09559,633174,376335,104
16619,985,0289.90%99,92559,437172,354331,716
16719,753,2379.90%98,76659,242170,351328,359
16819,523,6449.90%97,61859,048168,366325,032
16919,296,2309.90%96,48158,854166,401321,736
17019,070,9759.90%95,35558,661164,454318,470
17118,847,8599.90%94,23958,469162,526315,234
17218,626,8659.90%93,13458,277160,616312,027
17318,407,9729.90%92,04058,086158,724308,850
17418,191,1629.90%90,95657,895156,850305,702
17517,976,4169.90%89,88257,705154,995302,582
17617,763,7169.90%88,81957,516153,156299,491
17717,553,0439.90%87,76557,327151,336296,428
17817,344,3809.90%86,72257,139149,532293,394
17917,137,7089.90%85,68956,952147,746290,387
18016,933,0109.90%84,66556,765145,977287,408
18116,730,2679.90%83,65156,579144,225284,456
18216,529,4639.90%82,64756,393142,490281,531
18316,330,5809.90%81,65356,208140,771278,633
18416,133,6009.90%80,66856,024139,069275,761
18515,938,5079.90%79,69355,840137,383272,916
18615,745,2839.90%78,72655,657135,713270,097
18715,553,9139.90%77,77055,475134,060267,304
18815,364,3799.90%76,82255,293132,422264,536
18915,176,6649.90%75,88355,111130,800261,794
19014,990,7539.90%74,95454,931129,193259,077
19114,806,6309.90%74,03354,750127,602256,385
19214,624,2789.90%73,12154,571126,026253,718
19314,443,6819.90%72,21854,392124,466251,076
19414,264,8239.90%71,32454,213122,920248,457
19514,087,6909.90%70,43854,036121,389245,863
19613,912,2659.90%69,56153,858119,873243,293
19713,738,5339.90%68,69353,682118,372240,747
19813,566,4809.90%67,83253,506116,886238,223
19913,396,0889.90%66,98053,330115,413235,724
20013,227,3459.90%66,13753,155113,955233,247
20113,060,2359.90%65,30152,981112,511230,793
20212,894,7439.90%64,47452,807111,081228,362
20312,730,8559.90%63,65452,634109,665225,953
20412,568,5569.90%62,84352,461108,263223,567
20512,407,8329.90%62,03952,289106,874221,202
20612,248,6699.90%61,24352,118105,499218,860
20712,091,0539.90%60,45551,947104,137216,539
20811,934,9709.90%59,67551,776102,788214,239
20911,780,4059.90%58,90251,606101,453211,961
21011,627,3469.90%58,13751,437100,130209,704
21111,475,7799.90%57,37951,26898,821207,468
21211,325,6909.90%56,62851,10097,524205,252
21311,177,0669.90%55,88550,93396,240203,058
21411,029,8949.90%55,14950,76694,968200,883
21510,884,1609.90%54,42150,59993,709198,729
21610,739,8529.90%53,69950,43392,462196,594
21710,596,9579.90%52,98550,26891,228194,480
21810,455,4629.90%52,27750,10390,005192,385
21910,315,3549.90%51,57749,93888,795190,310
22010,176,6219.90%50,88349,77587,596188,254
22110,039,2509.90%50,19649,61186,409186,217
2229,903,2309.90%49,51649,44985,234184,199
2239,768,5479.90%48,84349,28684,070182,200
2249,635,1909.90%48,17649,12582,918180,219
2259,503,1479.90%47,51648,96481,778178,257
2269,372,4069.90%46,86248,80380,648176,313
2279,242,9559.90%46,21548,64379,530174,387
2289,114,7829.90%45,57448,48378,422172,480
2298,987,8779.90%44,93948,32477,326170,590
2308,862,2269.90%44,31148,16676,241168,718
2318,737,8209.90%43,68948,00875,166166,863
2328,614,6469.90%43,07347,85074,102165,025
2338,492,6949.90%42,46347,69373,048163,205
2348,371,9529.90%41,86047,53772,005161,402
2358,252,4109.90%41,26247,38170,972159,616
2368,134,0569.90%40,67047,22669,950157,846
2378,016,8819.90%40,08447,07168,938156,093
2387,900,8729.90%39,50446,91667,936154,357
2397,786,0209.90%38,93046,76366,944152,636
2407,672,3149.90%38,36246,60965,961150,932
2417,559,7439.90%37,79946,45664,989149,244
2427,448,2989.90%37,24146,30464,026147,572
2437,337,9689.90%36,69046,15263,073145,915
2447,228,7429.90%36,14446,00162,130144,274
2457,120,6129.90%35,60345,85061,196142,649
2467,013,5669.90%35,06845,69960,271141,038
2476,907,5969.90%34,53845,54959,356139,443
2486,802,6919.90%34,01345,40058,450137,863
2496,698,8419.90%33,49445,25157,553136,298
2506,596,0379.90%32,98045,10356,665134,748
2516,494,2709.90%32,47144,95555,786133,212
2526,393,5299.90%31,96844,80754,916131,691
2536,293,8069.90%31,46944,66054,054130,184
2546,195,0919.90%30,97544,51453,202128,691
2556,097,3769.90%30,48744,36852,358127,212
2566,000,6509.90%30,00344,22251,522125,748
2575,904,9069.90%29,52544,07750,695124,297
2585,810,1339.90%29,05143,93349,877122,860
2595,716,3239.90%28,58243,78949,067121,437
2605,623,4689.90%28,11743,64548,265120,027
2615,531,5589.90%27,65843,50247,471118,631
2625,440,5869.90%27,20343,35946,685117,247
2635,350,5419.90%26,75343,21745,908115,877
2645,261,4179.90%26,30743,07545,138114,520
2655,173,2039.90%25,86642,93444,376113,176
2665,085,8939.90%25,42942,79343,622111,845
2674,999,4789.90%24,99742,65342,876110,526
2684,913,9509.90%24,57042,51342,137109,220
2694,829,3009.90%24,14642,37341,406107,926
2704,745,5209.90%23,72842,23440,683106,645
2714,662,6039.90%23,31342,09639,967105,376
2724,580,5409.90%22,90341,95839,258104,119
2734,499,3249.90%22,49741,82038,557102,874
2744,418,9479.90%22,09541,68337,863101,640
2754,339,4029.90%21,69741,54637,176100,419
2764,260,6809.90%21,30341,41036,49699,209
2774,182,7739.90%20,91441,27435,82398,011
2784,105,6769.90%20,52841,13935,15896,825
2794,029,3799.90%20,14741,00434,49995,650
2803,953,8779.90%19,76940,86933,84794,486
2813,879,1609.90%19,39640,73533,20293,333
2823,805,2239.90%19,02640,60232,56492,191
2833,732,0589.90%18,66040,46831,93291,061
2843,659,6589.90%18,29840,33631,30789,941
2853,588,0169.90%17,94040,20330,68888,832
2863,517,1249.90%17,58640,07230,07687,733
2873,446,9779.90%17,23539,94029,47086,645
2883,377,5669.90%16,88839,80928,87185,568
2893,308,8869.90%16,54439,67928,27884,501
2903,240,9299.90%16,20539,54827,69283,445
2913,173,6899.90%15,86839,41927,11182,398
2923,107,1599.90%15,53639,28926,53781,362
2933,041,3339.90%15,20739,16025,96880,336
2942,976,2059.90%14,88139,03225,40679,319
2952,911,7669.90%14,55938,90424,85078,313
2962,848,0129.90%14,24038,77624,30077,316
2972,784,9379.90%13,92538,64923,75576,329
2982,722,5329.90%13,61338,52223,21675,351
2992,660,7949.90%13,30438,39622,68374,383
3002,599,7149.90%12,99938,27022,15673,425
3012,539,2889.90%12,69638,14521,63572,476
3022,479,5099.90%12,39838,01921,11971,536
3032,420,3719.90%12,10237,89520,60870,605
3042,361,8689.90%11,80937,77020,10369,683
3052,303,9949.90%11,52037,64719,60468,770
3062,246,7449.90%11,23437,52319,10967,866
3072,190,1119.90%10,95137,40018,62166,971
3082,134,0919.90%10,67037,27718,13766,085
3092,078,6769.90%10,39337,15517,65965,207
3102,023,8629.90%10,11937,03317,18664,338
3111,969,6439.90%9,84836,91216,71863,478
3121,916,0139.90%9,58036,79116,25562,626
3131,862,9689.90%9,31536,67015,79761,782
3141,810,5009.90%9,05336,55015,34460,947
3151,758,6069.90%8,79336,43014,89760,119
3161,707,2809.90%8,53636,31014,45459,300
3171,656,5169.90%8,28336,19114,01658,489
3181,606,3099.90%8,03236,07313,58257,686
3191,556,6549.90%7,78335,95413,15456,891
3201,507,5469.90%7,53835,83612,73056,104
3211,458,9809.90%7,29535,71912,31155,325
3221,410,9509.90%7,05535,60211,89754,553
3231,363,4529.90%6,81735,48511,48753,789
3241,316,4809.90%6,58235,36811,08153,032
3251,270,0309.90%6,35035,25210,68152,283
3261,224,0979.90%6,12035,13710,28451,542
3271,178,6769.90%5,89335,0229,89250,807
3281,133,7629.90%5,66934,9079,50550,080
3291,089,3519.90%5,44734,7929,12249,361
3301,045,4379.90%5,22734,6788,74348,648
3311,002,0169.90%5,01034,5648,36847,943
332959,0839.90%4,79534,4517,99847,244
333916,6349.90%4,58334,3387,63246,553
334874,6659.90%4,37334,2257,27045,868
335833,1709.90%4,16634,1136,91245,191
336792,1459.90%3,96134,0016,55844,520
337751,5869.90%3,75833,8906,20843,856
338711,4889.90%3,55733,7785,86243,198
339671,8489.90%3,35933,6685,52042,547
340632,6609.90%3,16333,5575,18241,903
341593,9219.90%2,97033,4474,84841,265
342555,6269.90%2,77833,3374,51840,633
343517,7709.90%2,58933,2284,19140,008
344480,3519.90%2,40233,1193,86939,389
345443,3649.90%2,21733,0103,55038,777
346406,8049.90%2,03432,9023,23438,170
347370,6679.90%1,85332,7942,92337,570
348334,9509.90%1,67532,6872,61536,976
349299,6499.90%1,49832,5792,31036,388
350264,7609.90%1,32432,4732,00935,806
351230,2789.90%1,15132,3661,71235,229
352196,2009.90%98132,2601,41834,659
353162,5229.90%81332,1541,12834,094
354129,2409.90%64632,04984133,536
35596,3519.90%48231,94455732,982
35663,8509.90%31931,83927732,435
35731,7349.90%15931,734031,893

Payment delay (agency pass-throughs pay investors several weeks after homeowners pay) is ignored.